Flux Conservation Research Articles

Propagation of a dome-shaped, large-scale extreme-ultraviolet wave in the solar corona

Context. The first observation of a dome-shaped extreme-ultraviolet (EUV) wave was recorded by the EUVI instrument on board the STEREO-B spacecraft on January 17, 2010. This observation has allowed us to study the three-dimensional propagation of a large-scale EUV wave in the solar corona, which is considered to be a manifestation of a large-amplitude magnetohydrodynamic (MHD) wave. Aims. These unique observations by EUVI offer the opportunity to compare the theory of large-amplitude MHD waves with observations. Methods. Nonlinear MHD equations were employed for describing large-amplitude fast magnetosonic waves in terms of so-called simple waves. Results. Measuring the velocity of the EUV wave across the solar surface allows us to determine the quiet Sun’s magnetic field to be ≈3.2 G. This magnetic field can be extrapolated to the corona by means of magnetic flux conservation. Then, the height dependence of the Alfvén velocity can be calculated, adopting an isothermal, gravitationally stratified density model with a temperature of 1.4 MK for the quiet corona. The Alfvén velocity has a local maximum of ≈680 km s−1 at a height of ≈1030 Mm above the photosphere. The observations show that the EUV wave initially steepens and subsequently decays during its further evolution along the solar surface. This behavior can be aptly explained in terms of simple MHD waves. Initially, the wave front steepens due to nonlinear effects. Since the EUV waves are circularly or spherically propagating waves in the corona, their amplitudes are decreasing during the evolution. Hence, the wave steepening vanishes at the final state of the evolution of the EUV wave, which is consistent with the observations. In reality, the nature of the considered EUV wave is a combination of that of a circular and a spherical wave in the corona. Conclusions. The propagation of this dome-shaped EUV wave can be well described by the theory of large amplitude (simple) MHD waves.

Synthesis of Elements in Compact Stars in Pycnonuclear Reactions with Carbon Isotopes: Quasibound States vs. States of Zero-Points Vibrations

(1) Purpose: Conditions of formation of compound nuclear systems needed for synthesis of heavy nuclei in pycnonuclear reactions in compact stars are studied on a quantum mechanical basis. (2) Methods: The method of multiple internal reflections is applied for pycnonuclear reactions in compact stars with new calculations of quasibound spectra and spectra of zero-point vibrations. (3) Results: Peculiarities of the method are analyzed for reaction with isotopes of Carbon. The developed method takes into account continuity and conservation of quantum flux (describing pycnonuclear reaction) inside the full spacial region of reaction, including the nuclear region. This gives the appearance of new states (called quasibound states) in which compound nuclear systems of Magnesium are formed with the largest probability. These states have not been studied yet in synthesis of elements in stars. Energy spectra of zero-point vibrations and spectra of quasibound states are estimated with high precision for reactions with isotopes of Carbon. For the first time, the influence of plasma screening on quasibound states and states of zero-point vibrations in pycnonuclear reactions has been studied. (4) Conclusions: The probability of formation of a compound nucleus in quasibound states in pycnonuclear reaction is essentially larger than the probability of formation of this system in states of zero-point vibrations studied by Zel’dovich and followers. Therefore, synthesis of Magnesium from isotopes of Carbon is more probable through the quasibound states than through the states of zero-point vibrations in compact stars. Energy spectra of zero-point vibrations are changed essentially after taking plasma screening into account. Analysis shows that from all studied isotopes of Magnesium, only 24Mg is stable after synthesis at an energy of relative motion of 4.881 MeV of the incident nuclei 12C.

A nonlinear scheme preserving maximum principle for heterogeneous anisotropic diffusion equation

We present a new nonlinear method in order to preserve the maximum principle for the diffusion problem with heterogeneous anisotropic coefficient. It is well-known that for diffusion problems with general discontinuous coefficients, the existing cell-centered finite volume schemes on general meshes cannot unconditionally satisfy the discrete maximum principle (DMP), i.e., there are always certain severe restrictions on the mesh-cell geometry or locations of discontinuity in order to preserve DMP. To deal with the issue we propose a nonlinear method of modifying discrete flux of linear second-order schemes into a new conservative flux. Then the resulting scheme keeps conservation and accuracy, and has the structure preserving maximum principle without imposing those severe restrictions. Specifically, we will start with the diamond scheme whose flux is linear and has second-order accuracy, but has no the structure preserving maximum principle. Then the nonlinear correction method is applied to get a scheme satisfying the discrete maximum principle unconditionally. We give some theoretical analysis including the coercivity property and a prior estimation. Numerical results show that the accuracy of our new scheme is superior to the existing scheme preserving maximum principle, and in some cases the accuracy can even be improved by one order of magnitude.

Formula omitted]-SGP: Scaled Gradient Projection with [formula omitted]-divergence for astronomical image restoration

Image restoration in astronomy has been considered a vital step in many ground-based observational programs that often suffer from sub-optimal seeing due to atmospheric turbulence, distortion of stellar shapes due to instrumental aberrations, trailing, and other issues. It holds importance for various tasks: improved astrometry, deblending of overlapping sources, faint source detection, and identification of point sources near bright extended objects, such as galaxies, to name a few. We conduct an empirical study by applying the Scaled Gradient Projection (SGP) iterative image deconvolution algorithm to restore distorted stellar shapes in our observed data. We investigate using a more flexible divergence measure, the β-divergence, which contains the commonly-used Kullback–Leibler (KL) divergence as a special case and allows automatic adaptation of the parameter β to the data. An extensive set of experiments comparing the performance of SGP and its β-divergence variant (β-SGP) is carried out on extracted star stamps and on images containing multiple stars (both crowded and relatively sparser fields). We show a consistent enhancement in the flux conservation across all considered scenarios using β-SGP compared to SGP. Using a few quantifiable metrics such as the Full-Width-at-Half-Maximum (FWHM) and ellipticity of stars, we observe that β-SGP improves restoration quality, compared to the SGP, in many cases and still preserves restoration quality in others. We conclude that generalized versions of image restoration algorithms are more robust due to their enhanced flexibility and could be a promising modification for astronomical image restoration.

Investigation of scaling criteria and matching method of overall cooling effectiveness with thermal radiation

Ever-improving gas temperature and infrared stealth requirements for aero engines will make thermal radiation become a vital contribution to total heat transfer. To evaluate the cooling performance in laboratory conditions, the corresponding scaling criteria, and matching methods of overall cooling effectiveness (Φ) considering thermal radiation need to be studied. In this paper, a one-dimensional, simplified heat transfer analysis expression with thermal radiation was derived based on the principle of heat flux conservation. The scaling criterion about radiation (radiation Biot number: Bir) was proposed. The scaling criteria of Φ were established to guide experiments conducted reveal the Φ in actual engine condition. These criteria were well verified with an impingement-effusion model applied afterburner heat shield by conjugate radiation simulations. Two matching methods of Bir in scaling criteria were proposed and investigated in detail, which include adjusting the power of the radiation source alone and coating high emissivity paint combined with a lower power radiation source. The results indicate that thermal radiation has a very remarkable effect on Φ of the film plate. The area-average Φ decreased by 22.8%, 15.9%, 12.5% and 10.4% for blowing ratio M = 0.2, 0.4, 0.6 and 0.8, respectively. The Bir and Φ can be accurately matched under laboratory conditions using the two matching methods. The relative matching deviation of Φ between the laboratory and the engine conditions is less than 3%.

High-order methods for hypersonic flows with strong shocks and real chemistry

We compare high-order methods including spectral difference (SD), flux reconstruction (FR), the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal discontinuous Galerkin methods, and WENO to select the best candidate to simulate strong shock waves characteristic of hypersonic flows. We consider several benchmarks, including the Leblanc and modified shock-density wave interaction problems that require robust stabilization and positivity-preserving properties for a successful flow realization. We also perform simulations of the three-species Sod problem with simplified chemistry with the chemical reaction source terms introduced in the Euler equations. The ES-DGSEM scheme exhibits the highest stability, negligible numerical oscillations, and requires the least computational effort in resolving reactive flow regimes with strong shock waves. Therefore, we extend the ES-DGSEM to hypersonic Euler equations by deriving a new set of two-point entropy conservative fluxes for a five-species gas model. In this paper, hypersonic Euler equations refer to the multi-species Euler equations for which the internal energy and thermodynamic properties are computed using the Rigid-Rotor Harmonic-Oscillator model. Stabilization for capturing strong shock waves occurs by blending high-order entropy conservative fluxes with low-order finite volume fluxes constructed using the HLLC Riemann solver. The hypersonic Euler solver is verified using the non-equilibrium chemistry Sod problem. To this end, we adopt the Mutation++ library to compute the reaction source terms, thermodynamic properties, and transport coefficients. We also investigate the effect of real chemistry versus ideal chemistry, and the results demonstrate that the ideal chemistry assumption fails at high temperatures, hence real chemistry must be employed for accurate predictions. Finally, we consider a viscous hypersonic flow problem to verify the transport coefficients and reaction source terms determined by the Mutation++ library.

Motion of localized disturbances in scalar harmonic lattices.

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Higher-form symmetries, anomalous magnetohydrodynamics, and holography

In U(1)U(1) Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator F_{\mu\nu} \tilde{F}^{\mu\nu}FμνF̃μν constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

Conservation of heat and mass in P-SKRIPS version 1: the coupled atmosphere–ice–ocean model of the Ross Sea

Abstract. Ocean–atmosphere–sea ice interactions are key to understanding the future of the Southern Ocean and the Antarctic continent. Regional coupled climate–sea ice–ocean models have been developed for several polar regions; however the conservation of heat and mass fluxes between coupled models is often overlooked due to computational difficulties. At regional scale, the non-conservation of water and energy can lead to model drift over multi-year model simulations. Here we present P-SKRIPS version 1, a new version of the SKRIPS coupled model setup for the Ross Sea region. Our development includes a full conservation of heat and mass fluxes transferred between the climate (PWRF) and sea ice–ocean (MITgcm) models. We examine open water, sea ice cover, and ice sheet interfaces. We show the evidence of the flux conservation in the results of a 1-month-long summer and 1-month-long winter test experiment. P-SKRIPS v.1 shows the implications of conserving heat flux over the Terra Nova Bay and Ross Sea polynyas in August 2016, eliminating the mismatch between total flux calculation in PWRF and MITgcm up to 922 W m−2.

Insights into inactivation and response mechanisms of sublethal Listeria monocytogenes treated by cold plasma with joint transcriptomics and metabolomics

The aim of the current study is to elucidate the inactivation and molecular response pattern of sublethal Listeria monocytogenes to cold plasma mediated two-pronged oxidative microenvironments from a high-throughput multi-omics perspective. First joint transcriptomics and metabolomics analyses revealed that significantly expressed genes and metabolites were mainly involved in enhanced transmembrane transport and Fe2+/Cu+ efflux, amino acids limitation, cytoplasmic pH homeostasis, reconfiguration of central carbon metabolism flux and energy conservation strategy, which triggered the surge of intracellular endogenous oxidative stress and finally mediated bacterial ferroptosis and pathogenicity attenuation. Typical antioxidant systems such as the TrxR-Trx system and common antioxidant genes (e.g. sodA, katA, ahpC, trxA, spxA) were inhibited, and the more prominent antioxidant pathways include methionine metabolism, pentose phosphate pathway and glutathione metabolism as well as the DNA repair systems. Therefore, our work confirmed from the transcriptional and metabolic as well as physiological levels that cold plasma-mediated intracellular oxidative stress induced big perturbations in pathways as a driving force for the inactivation and pathogenicity attenuation of L. monocytogenes.

Electromagnetic electron Kelvin–Helmholtz instability

On electron kinetic scales, ions and electrons decouple, and electron velocity shear on electron inertial length ∼de can trigger electromagnetic (EM) electron Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in an inviscid collisionless plasma with a step-function electron shear flow. We show that in incompressible collisionless plasma, the ideal electron frozen-in condition E+ve×B/c=0 must be broken for the EM EKHI to occur. In a step-function electron shear flow, the ideal electron frozen-in condition is replaced by magnetic flux conservation, i.e., ∇×(E+ve×B/c)=0, resulting in a dispersion relation similar to that of the standard ideal and incompressible magnetohydrodynamics KHI. The magnetic field parallel to the electron streaming suppresses the EM EKHI due to magnetic tension. The threshold for the EM mode of the EKHI is (k·ΔUe)2>ne1+ne2ne1ne2[ne1(vAe1·k)2+ne2(vAe2·k)2], where vAe=B/(4πmene)1/2, ΔUe, and ne are the electron streaming velocity shear and densities, respectively. The growth rate of the EM mode is γem∼Ωce, which is the electron gyro-frequency.

Conservation laws and Hamiltonian of the nonlinear Schrödinger equation of the fourth order with arbitrary refractive index

Objective:Conservation laws of the generalized nonlinear Schrödinger equation with arbitrary refractive index of the fourth order are found. Conservative quantities corresponding to the bright optical soliton are calculated. Method:Direct calculations of three conservation laws for the considered equation are used. This approach allows us to obtain the conservative densities and fluxes of the equation. Results:It is shown that there exist three conservation laws corresponding to the studied equation. The bright optical solitons of the equation are obtained. Using these solutions, conservative quantities of the soliton for the equation are calculated by means of integration. Some properties of conservation laws are discussed.

Sign stable arbitrary high order reconstructions for constructing non-oscillatory entropy stable schemes

High order sign stable reconstructions are much sought after to develop high order non-oscillatory entropy stable schemes. This work presents a very simple but generic approach to construct arbitrary high order sign stable reconstructions. Further, by utilizing such obtained sign stable reconstructions entropy stable schemes are constructed using well known arbitrary high-order entropy conservative fluxes. Several numerical results for 1D and 2D benchmark test problems are given to demonstrate the accuracy and non-oscillatory property of representative entropy stable schemes which are designed using of proposed approach.

Verifying Ray Tracing Amplitude Methods for Global Magnetospheric Modeling

AbstractRay tracing is a commonly used method for modeling the propagation of electromagnetic waves in Earth's magnetosphere. To apply ray tracing results to global models of wave‐particle interaction such as energetic electron scattering, it is useful to map the discrete rays to a volume filling mesh. However, some methods have inherent losses of energy from the wave source, or do not account for the full range of wave properties within a sample volume. We have developed and tested a 3D magnetospheric ray tracing code “MESHRAY” which resolves these issues. MESHRAY uses the conservation of Poynting flux through ray triplets with finite volume to determine the local field amplitudes. Electromagnetic wave energy density from all ray data points is mapped to a mesh and verified against the wave source power for energy conservation varying time step length, number of rays, and total time steps. We find that the method is self‐consistent and numerically robust. We further investigate whether the neglect of phase information and superposition has a significant impact on the accuracy of mapping wave intensity to a mesh. We find excellent agreement between the analytic solution for waves emitted by a line source in a plane‐stratified medium and an equivalent ray tracing solution. When phase information is excluded, ray tracing reproduces an average amplitude spread over regions of coherent constructive and destructive interference. This may be an important consideration for interpolating ray tracing results of longer wavelength waves such as magnetosonic, electromagnetic ion cyclotron, or ULF waves.

A positivity-preserving and conservative high-order flux reconstruction method for the polyatomic Boltzmann–BGK equation

In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann–BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Through modeling the internal degrees of freedom, the approach is further extended to polyatomic molecules and can encompass arbitrary constitutive laws. The approach is validated on a series of large-scale complex numerical experiments, ranging from shock-dominated flows computed on unstructured grids to direct numerical simulation of three-dimensional compressible turbulent flows, the latter of which is the first instance of such a flow computed by directly solving the Boltzmann equation. The results show the ability of the scheme to directly resolve shock structures without any ad hoc numerical shock capturing method and correctly approximate turbulent flow phenomena in a consistent manner with the hydrodynamic equations.

Formal Derivations of Mode Coupling Equations in Underwater Acoustics: How the Method of Multiple Scales Results in an Expansion over Eigenfunctions and the Vectorized WKBJ Solution for the Amplitudes

In this study formal derivation of mode coupling equations in underwater acoustics is revisited. This derivation is based on the method of multiple scales from which modal expansion of the field emerges, and the vectorized WKBJ equation for the coefficients in this expansion are obtained in an automatic way. Asymptotic analysis accomplished in this work also establishes a connection between coupled mode parabolic equations in three-dimensional case and the generalized WKBJ solution that emerges as its two-dimensional counterpart. Despite the fact that similar mode coupling equations can be found in literature, in our study a new systematic and formalized approach to their derivation is proposed. A theorem that guarantees asymptotic conservation of the energy flux in the considered two-dimensional waveguide is also proven.

Shafranov shift correction to the Furth–Yoshikawa scaling of tokamak adiabatic compression

In 1970, Furth and Yoshikawa (1970 Phys. Fluids 13 2593–6) introduced the scalings of adiabatic plasma compression. Basically, if the shape of the external plasma boundary and the aspect ratio are preserved during the compression, then the density, kinetic pressure, beta and current scale respectively as , , , , , where C is the linear compression ratio, that is, the ratio between initial and final major radii. In this work, we show analytically, by expanding the Grad–Shafranov equation in terms of C, that the deviation to the Furth–Yoshikawa scaling is related to the Shafranov shift that arises when beta increases at large compression ratios. There is an obvious effect of the Shafranov shift because the axis is moved to a region with larger volume element, and an indirect effect, associated to the relation between flux and radius. The latter effect adds to the first, and is of the same order of magnitude. The result is that the pressure increases less than the C 5 scaling, which can have a significant impact on the fusion power achieved at maximum compression. The analytical results are backed up by equilibrium simulations carried out with the CHEASE code. Equilibria are obtained for different values of C, with conservation of the total fluxes, q profile, and entropy of the plasma. The agreement of the theory and simulations is very good when the boundary of the plasma is circular and the aspect ratio small. When the aspect ratio is close to 1, and/or the boundary not circular, the analytical result gives the gist of the reduction of compression. Finally, a pressure anisotropy approximately equal to the increase in normalized Shafranov shift is predicted.

Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick's Law Model of Diffusion.

To investigate the impact of experimental interventions on living biological tissue, ex vivo rodent brain slices are often used as a more controllable alternative to a live animal model. However, for meaningful results, the biological sample must be known to be healthy and viable. One of the gold-standard approaches to identifying tissue viability status is to measure the rate of tissue oxygen consumption under specific controlled conditions. Here, we work with thin (400 μm) slices of mouse cortical brain tissue which are sustained by a steady flow of oxygenated artificial cerebralspinal fluid (aCSF) at room temperature. To quantify tissue oxygen consumption (Q), we measure oxygen partial pressure (pO2) as a function of probe depth. The curvature of the obtained parabolic (or parabola-like) pO2 profiles can be used to extract Q, providing one knows the Krogh coefficient Kt, for the tissue. The oxygen trends are well described by a Fick's law diffusion-consumption model developed by Ivanova and Simeonov, and expressed in terms of ratio (Q/K), being the rate of oxygen consumption in tissue divided by the Krogh coefficient (oxygen diffusivity × oxygen solubility) for tissue. If the fluid immediately adjacent to the tissue can be assumed to be stationary (i.e., nonflowing), one may invoke conservation of oxygen flux K·(∂P/∂x) across the interface to deduce (Kt/Kf), the ratio of Krogh coefficients for tissue and fluid. Using published interpolation formulas for the effect of salt content and temperature on oxygen diffusivity and solubility for pure water, we estimate Kf, the Krogh coefficient for aCSF, and hence deduce the Kt coefficient for tissue. We distinguish experimental uncertainty from natural biological variability by using pairs of repeated profiles at the same tissue location. We report a dimensionless Krogh ratio (Kt/Kf)=0.562±0.088 (mean ± SD), corresponding to a Krogh coefficient Kt=(1.29±0.21)×10-14 mol/(m·s·Pa) for mouse cortical tissue at room temperature, but acknowledge the experimental limitation of being unable to verify that the fluid boundary layer is truly stationary. We compare our results with those reported in the literature, and comment on the challenges and ambiguities caused by the extensive use of 'biologically convenient' non-SI units for tissue Krogh coefficient.

Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods

AbstractA common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. In this article, we present a novel framework for partitioned heterogeneous time‐integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial‐in‐time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time‐integrators for the individual subproblems without compromising the time‐accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time‐integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air‐sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time‐integrators from the explicit Runge‐Kutta and Adams‐Moulton families.

A 1-D/3-D coupling approach for compressible non-equilibrium two-phase flows using the Baer-Nunziato model based on the Finite-Volume framework

An efficient bi-directional 1-D/3-D coupling is here proposed for the computation of compressible two-phase flows with the use of the Baer-Nunziato model. The objective is here to couple the 3-D Baer-Nunziato model with its 1-D counterpart involving spatially varying pipe cross-sections. The present coupling acts at the common interface between three-dimensional and one-dimensional computational domains. The proposed approach is built upon the framework of the Finite-Volume method with, in particular, the exchange of the numerical fluxes coming from the approximation of both conservative and non-conservative terms of the convective part of the Baer-Nunziato model. For this purpose, local Riemann problems at the 1-D/3-D common interface are considered for the computation of the corresponding numerical conservative and non-conservative fluxes. These local Riemann problems are based on the variables associated with the 1-D domain on one side and the variables coming from the 3-D domain on the other side of the interface. The potentially non-null tangential phasic velocity components coming from the 3-D domain at the coupling interface are also considered in the local Riemann problems. In addition, adequate approximations of the non-conservative terms associated with changes of volume fraction as well as changes of cross-section are considered at the 1-D/3-D interface. As a consequence, conservation properties such as the uniform pressure and velocity profiles preservation are ensured by the present 1-D/3-D coupling. The pipe cross-section variations are also taken into account in the present method. What is more, no iterative procedure is required in the proposed approach. Several numerical shock-tubes involving both subsonic and supersonic configurations of the Baer-Nunziato model and pipe cross-section variations are then considered to assess the present 1-D/3-D coupling. The influence of the angle between the 1-D and the 3-D domains at the coupling interface is also studied. Finally, the propagation of a shock-wave in a circular tube with a sudden change in cross-section is simulated using a hybrid 1-D/3-D computation showing the potential of the proposed geometrical multi-scale strategy.